A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS

Volume: 9 Number: 4 December 1, 2019
  • K. Günel
  • İ. Gör
EN

A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS

Abstract

In this paper, some improvements have been made on Arti cial Bee Colony ABC algorithm to get numerical solutions of both linear and nonlinear di erential equations as initial value problems. The solutions are obtained by a feed-forward neural network trained by the modi ed ABC.

Keywords

References

  1. Lee, H. and Kang, I. 1990. Neural algorithms for solving differential equations, Journal of Computa- tional Physics, 91, 110.
  2. Malek, A. and Beidokhti, R.S. 2006. Numerical solution for high order differential equations using a hybrid neural network-optimization method, Applied Mathematics and Computation, 183, 260-271.
  3. Lagaris, I. E., Likas, A. and Fotiadis, D. I. 1998. Artificial neural networks for solving ordinary and partial differential equations, IEEE Transactions on Neural Networks, 9(5), 987-1000.
  4. Aarts, L. P. and Van Der Veer, P. 2008. Neural Network Method for Solving Partial Differential Equations, Neural Process. Lett., 14(3), 261-271.
  5. McFall, K. S. and Mahan, J. R. 2009. Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions, IEEE Transactions On Neural Networks, 20(8).
  6. Beidokhti, R. S. and Malek A. 2009. Solving initial-boundary value problems for systems of PDE using NN and optimization techniques, Journal of the Franklin Institute, 346, 898–913.
  7. Tsoulos, G. I., Gavrillis, D. and Glavas, E. 2009. Solving differential equations with constructed neural networks, Neurocomputing, 72, 2385-2391.
  8. Anastassi, A. A. 2014. Constructing Runge–Kutta methods with the use of artificial neural networks, Neural Computing and Applications, 25, 229-236.

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

K. Günel This is me

İ. Gör This is me

Publication Date

December 1, 2019

Submission Date

-

Acceptance Date

-

Published in Issue

Year 2019 Volume: 9 Number: 4

APA
Günel, K., & Gör, İ. (2019). A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS. TWMS Journal of Applied and Engineering Mathematics, 9(4), 810-821. https://izlik.org/JA83DT36CB
AMA
1.Günel K, Gör İ. A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS. JAEM. 2019;9(4):810-821. https://izlik.org/JA83DT36CB
Chicago
Günel, K., and İ. Gör. 2019. “A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS”. TWMS Journal of Applied and Engineering Mathematics 9 (4): 810-21. https://izlik.org/JA83DT36CB.
EndNote
Günel K, Gör İ (December 1, 2019) A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS. TWMS Journal of Applied and Engineering Mathematics 9 4 810–821.
IEEE
[1]K. Günel and İ. Gör, “A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS”, JAEM, vol. 9, no. 4, pp. 810–821, Dec. 2019, [Online]. Available: https://izlik.org/JA83DT36CB
ISNAD
Günel, K. - Gör, İ. “A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS”. TWMS Journal of Applied and Engineering Mathematics 9/4 (December 1, 2019): 810-821. https://izlik.org/JA83DT36CB.
JAMA
1.Günel K, Gör İ. A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS. JAEM. 2019;9:810–821.
MLA
Günel, K., and İ. Gör. “A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS”. TWMS Journal of Applied and Engineering Mathematics, vol. 9, no. 4, Dec. 2019, pp. 810-21, https://izlik.org/JA83DT36CB.
Vancouver
1.K. Günel, İ. Gör. A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS. JAEM [Internet]. 2019 Dec. 1;9(4):810-21. Available from: https://izlik.org/JA83DT36CB